Question: What's the first wrong statement in the proof below that $ \triangle BCA \cong \triangle BCE$ $ \; ?$ $ \overline{BC} $ is parallel to $ \overline{DF} $. This diagram is not drawn to scale. A B C D E F Givens $ \overline{DE} \cong \overline{AC}$ $, \ $ $ \angle BDE \cong \angle ACB$ $, \ $ $ \angle DBE \cong \angle ABC$ $, \ $ $ \angle CFE \cong \angle ABC$ $, \ $ $ \overline{EF} \cong \overline{AB}$ $, \ $ and $\ $ $ \angle CEF \cong \angle BAC$ Proof $ \triangle BCA \cong \triangle BDE$ because AAS $ \overline{AB} \cong \overline{BE}$ because corresponding parts of congruent triangles are congruent $ \triangle BDE \cong \triangle FCE$ because SSS $ \triangle BCA \cong \triangle FCE$ because ASA $ \angle BED \cong \angle BAC$ because corresponding parts of congruent triangles are congruent $ \triangle BCA \cong \triangle BCE$ because SSS
Try going through the proof yourself: write down the givens, and then see if they justify the next step for the reason given. Then do the same thing for the next step, and the next, until you run into something that you can't justify, or you finish the proof. $ \triangle FCE \cong \triangle BDE$ is the first wrong statement.